Model parameters neural network. It consists of layers of interconnected neurons or nodes.
layers import Input, Dense, SimpleRNN, LSTM, GRU, Conv2D from keras. It works by computing the gradient of the objective function with respect to a mini-batch of training examples and updating the model parameters in the direction of the negative gradient. We define the activation function and its role in capturing nonlinear patterns in the input data. 2. compile() —the final method that trains the neural network. The data are used to train neural networks which provide a good initial guess for the model parameters. . At the end of the learning process, model parameters are what constitute the model itself. In this case, these parameters are learned during the training stage. We focus on the most important lens mass model parameters, namely, the Einstein radius, the axis ratio and the position angle of the major axis of the mass distribution. This issue can be addressed through hyperparameter tuning, which involves adjusting various parameters to optimize the performance of the model. Weights in ANNs are analogous to the synapses in biological neural networks. This paper presents a novel approach known as the cross estimation network Dec 20, 2020 · This paper investigates the possibility of using Artificial Neural Networks (ANN) to reliably identify tire model parameters. Examples of parameters. A single-layer artificial neural network, also called a single-layer, has a single Oct 18, 2019 · X = w_1*x_1 + w_2*x_2 = w_1*g (weighted sum of all inputs) + w_2*g (weighted sum of all inputs) That is the function estimated by a neural network with N inputs, 2 neurons on the input layer and one neuron on the output layer. 9. Note that in deep neural networks, we’re dealing with millions of parameters, but the basic principle stays the same. Defaults to True. Neurons work like this: They receive one or more input signals. Some examples of model hyperparameters include: The learning rate for training a neural network. Network components include neurons, connections, weights, biases, propagation functions, and a learning rule. The nodes in neural networks are composed of parameters referred to as weights used to calculate a weighted sum of the inputs. Jan 14, 2022 · Abstract. compile() , as in the above example, or you can pass it by its string identifier. Since many DNN models are developed based on public datasets and pre-trained models often published by untrusted third parties, backdoors can be easily injected. The setting of parameters and the results of 20 random experiments are listed in the Table 2. This neural network requires a sequence of time instances as direct input of the network and the numbers of susceptibles, vaccinated, infected, hospitalized, and recovered individuals per We use in silico experiments to create a large set of training data in a span that covers real-life scenarios. They are comprised of a large number of connected nodes, each of which performs a simple mathematical operation. The coefficients (or weights) of linear and logistic regression models. These weights and biases are indeed learnable parameters. For example: 1. It consists of layers of interconnected neurons or nodes. Dec 10, 2018 · This paper proposes a new logarithmic quantization algorithm to mitigate the deterioration on neural networks which contain layers of small size and achieves the minimum accuracy loss on GoogLeNet after direct quantization compared to quantized counterparts. Dec 1, 2023 · This study proposes an application of a neural network methodology to estimate the parameters of the MR damper algebraic model. Use a larger network. compile(loss='mse', optimizer='sgd') The loss function can be inputed either as a String — as shown above — or as a function object — either imported from TensorFlow or written Aug 28, 2020 · I need to reinstate the model to an unlearned state by resetting the parameters of the neural network. Yields (str, Parameter) – Tuple containing the name and parameter. I want to see if any training happens, or if some other reason causes the results to be the same. The Adam optimization algorithm is an extension to stochastic gradient descent that has recently seen broader adoption for deep learning applications in computer vision and natural language processing. To get the parameter count of each layer like Keras, PyTorch has model. If all we did was multiple tensors by layer weights repeatedly, we could only simulate linear functions; further, there would be no point to having many layers, as the whole network would reduce could be reduced to a single matrix multiplication. The model will randomly remove 50% of the units from each layer and we finally end up with a much simpler network: Feb 11, 2019 · Parameters in general are weights that are learnt during training. In [ 20 ], a surrogate model is developed using polynomial chaos expansion for the determination of static and dynamic simulation parameters of dams. # Update the parameter. The input layer contains the coordinates of the drilling point, the depth of the predicted point, and the phase code output layer is a type of parameter of the rock and soil. You’ll do that by creating a weighted sum of the variables. Specifically, we analyze parameter distributions in a deep model and perform sampling to map them onto a low-dimensional parameter manifold using the local tangent space alignment (LTSA). Jul 5, 2024 · They are required for estimating the model parameters. We use data from model simulations as input and train deep neural networks Dec 7, 2023 · Hyperparameter Tuning. Moreover, it is unclear exactly how many parameters a neural network needs to fit its training set in practice. copy_(transformed_param) If you want to only update weights instead of every parameter: # Don't update if this is not a weight. Mar 31, 2021 · The benefits of using CNNs over other traditional neural networks in the computer vision environment are listed as follows: 1. In this regard, a SNN model containing six neural networks, corresponding to the six model parameters (c, k, α, β, δ, and F 0), is developed to predict the parameters of the hyperbolic algebraic model. models import Model. In Nov 3, 2023 · To represent the elasto-plastic behavior of steel, a neural network is used as a surrogate model with a genetic algorithm for parameter identification in . 4 days ago · Overfitting is a pervasive problem in neural networks, where the model becomes too specialized to the training data and fails to generalize well to new, unseen data. Input layer: All the input layer does is read the input image, so there are no parameters you could learn here. So in total, the amount of parameters in this neural network is The obvious benefit of having many parameters is that you can represent much more complicated functions than with fewer parameters. Model the input layer according to the no. The NNA is employed to minimize adopted objective function, which is formulated as the sum of squared deviations (SSD) between the actual data and estimated voltage points subjects to set of Dec 3, 2019 · Batch normalization is a technique for training very deep neural networks that standardizes the inputs to a layer for each mini-batch. making your data look big just by using The choice of optimization algorithm for your deep learning model can mean the difference between good results in minutes, hours, and days. Remove ads. May 11, 2020 · A multiple regression and machine learning approach is proposed to solve multiple plasma parameter inversion in complex systems. Update each parameter using the gradients, according to the optimization algorithm; Then, given a new data point, you can use the model to predict its class. Sep 28, 2022 · Therefore, random initialization is done to the parameters. Define the neural network that has some learnable parameters (or weights) Iterate over a dataset of inputs. 2 We construct training examples by using the econometric model to simulate datasets under a range of parameter values. Then, to multiply all parameters by 0. In addition, existing compression algorithms highly rely on retraining which requires heavy computational power. The model has the following structure: st ot = tanh(Uxt + Wst−1) = softmax(Vst) s t = tanh. param. The May 28, 2022 · The overall dimensions of the greenhouse are 12. May 3, 2021 · Sensitivity analysis of urban flood model parameters is important for urban flood simulation. 9: # Transform the parameter as required. This structure encompasses a set of parameters to adjust to perform specific tasks. Based on the fact that parameters of pre-trained neural networks naturally have non-uniform distributions, logarithmic quantization of Oct 1, 2023 · In this work, we propose to explore the intrinsic low-dimensional manifold of network parameters for efficient model optimization. , 1992 ) is a training algorithm with random parameters for SLFNs, where the basic network structure is presented in Fig. In this post, you will discover the batch normalization method Sep 15, 2022 · Thus, finding the optimal parameter design is one of the important parts of the training of the convolutional neural network. We perform a sensitivity analysis of the model parameters, where sensitivity means the influence degree of the model parameters on the characteristic curves Aug 9, 2017 · A probability too low has minimal effect and a value too high results in under-learning by the network. Apr 12, 2020 · Feature extraction with a Sequential model. Apr 25, 2024 · A neural network is a computational model inspired by the structure and function of the human brain. They are set manually. The learning rate determines the step size takenin the directionof thegradient. Aug 26, 2019 · The amount of parameters (meaning weights and bias that make up the cost function) is then: For the weights: $$784\times 16+16\times16+16\times10=12960$$ For the bias components: We have $32$ neurons in the hidden layers and $10$ in the output, so we have $$32+10 = 42$$ biases. The estimated parameters can be used as initial estimations for more sophisticated, but local identification algorithms. Return type. We show how to estimate parameters from max-stable processes, where inference is exceptionally challenging even with small datasets but simulation is straightforward. The final parameters found after training will decide how the model will perform on unseen data. Jan 3, 2024 · Neural networks extract identifying features from data, lacking pre-programmed understanding. The following are the steps involved in modeling and training a neural network. So before going ahead let’s install and import the TensorFlow module. Jan 21, 2019 · Convolutional Neural Network (CNN) In parallel, I will build the model with APIs from Keras for easy prototyping and a clean code so let’s quickly import the relevant objects here: from keras. The first thing you’ll need to do is represent the inputs with Python and NumPy. when a linear model has a unique optimal parameter vector. They are the parameters that are adjusted during the training process to minimize the difference Aug 31, 2023 · In machine learning, neural networks are a biologically inspired computational model that consists of a network architecture composed of artificial neurons. However, recent research has revealed that intentionally adding some perturbations to the input samples of a DNN can cause the model to misclassify the samples. The choice of the deep neural network will likely depend on the type of input and output. weight) torch. Using the pip/conda command to install TensorFlow in your system. To extract network model parameters from recordings of neural activity such as the LFP, the network model parameters must necessarily be reflected in these recordings. deep neural networks. Model the output layer according to the no. transformed_param = param * 0. Feb 28, 2022 · Now, creating a neural network might not be the primary function of the TensorFlow library but it is used quite frequently for this purpose. In order to quickly obtain the sensitive runoff parameters of the urban flood simulation model, this study proposes an artificial neural network-based identification method for sensitive parameters Thus, finding the optimal parameter design is one of the important parts of the training of the convolutional neural network. Feb 24, 2024 · A novel neural network model for forecasting the life of a dry gas pipeline system and detecting the metal loss dimension class that is exposed to a harsh environment is presented in this study to Jul 19, 2020 · There is one more technique we can use to perform regularization. 1. Hyperparameters determine how well your neural network learns and processes information. Sep 14, 2020 · Mathematically, a feed-forward neural network defines a mapping y = f(x; θ) and learns the value of the parameters θ that helps in finding the best function approximation. In the context of artificial neural networks (ANNs), weights are a fundamental component that play a crucial role in the network's ability to learn and make predictions. “Classifier” and “Regressor” refer to the task that each MLP can be neural network; see Section IV-C3. Neural network models are fit using an optimization algorithm called stochastic gradient descent that incrementally changes Jul 29, 2021 · We propose to use deep learning to estimate parameters in statistical models when standard likelihood estimation methods are computationally infeasible. of classes in the output. Here we give details on the specific form assumed for F w in (2) responsible for learning the mapping between simulated data (input) and the statistical model parameters (output) of the deep NN. SGD has beenshown Dec 16, 2023 · The Polarizable atom interaction Neural Network (PaiNN), an equivariant message-passing NN was used to learn the interatomic potentials 12, given its balance between speed and accuracy. The neural net takes a dataset as input and tries to recognize the parameter value underlying that dataset. . Mar 16, 2017 · The parameters of a neural network are typically the weights of the connections. Nov 15, 2017 · The resulting Bayesian neural networks can capture the posterior probabilities of the weights, yielding well-defined estimates of uncertainties. Model parameters are learned during training. 72 m 3, and the surface of the cover (A c) is 461. nn. fc2. How to Train and Model a Neural Network . Sep 11, 2019 · The model we will define has one input variable, a hidden layer with two neurons, and an output layer with one binary output. e. In the case of LSTMs, it may be desirable to use different dropout rates for May 16, 2021 · Regarding the neural network architecture, "the backbone is a modified ResNet 50", that is, a convolutional network. During the training process, we've discussed how stochastic gradient descent, or SGD, works to learn and optimize the weights and biases in a neural network. 8 m 2, the total volume (V) is 798. # pip. Inside the model architecture, we’ll include variables for the number of nodes in a given layer and dropout rate. 5 m and 3. Details of Mar 8, 2016 · 7. The defender usually cannot access training data and does not know the target class or the Mar 9, 2018 · 87. ” Mar 10, 2020 · Model behaviour across parameter space. In the latter case, the default parameters for the optimizer will be used. This is called the property of “consistency. Iterator[Tuple[str, Parameter]] Example: Jul 30, 2023 · Deep neural networks (DNNs) have been widely deployed in a diverse array of tasks, such as image classification. It can be used with most, perhaps all, types of neural network models, not least the most common network types of Multilayer Perceptrons, Convolutional Neural Networks, and Long Short-Term Memory Recurrent Neural Networks. Connections involve weights and biases regulating information transfer. Mar 14, 2017 · Let's first look at how the number of learnable parameters is calculated for each individual type of layer you have, and then calculate the number of parameters in your example. remove_duplicate (bool, optional) – whether to remove the duplicated parameters in the result. pip install tensorflow --upgrade. Apr 29, 2024 · In this work, we build and train a simple convolutional neural network with an aim to rapidly predict model parameters of gravitational lenses. Neurons receive inputs, governed by thresholds and activation functions. Otherwise, yields only parameters that are direct members of this module. Source: Yoshua Bengio. We describe the inspiration for artificial neural networks and how the methods of deep learning are built. The code listing for this network is provided below. [1 input] -> [2 neurons] -> [1 output] If you are new to Keras or deep learning, see this step-by-step Keras tutorial. init. Hyperparameters are settings that control the learning process of the model, such as the learning rate, the number of neurons in a neural network, or the kernel size in a support vector machine. If xt = {0, 1}m x t = { 0, 1 } m and U is a n × Sep 1, 2023 · Introduction to convolutional neural networks. However, models of such DNN often have massive trainable parameters, which lead to big resource burden in practice. These attributes can be used to do neat things, like quickly creating a model that extracts the outputs of all intermediate layers in a Sequential model: Dec 30, 2020 · The learning algorithm is continuously updating the parameter values as learning progress but hyperparameter values set by the model designer remain unchanged. 5 to all these images. The initialization step can be critical to the model’s ultimate performance, and it requires the right method. The relationships that neural networks model are often very complicated ones and using a small network (adapting the size of the network to the size of the training set, i. In this paper, we analyse in depth the attributes of logarithmic quantization. The PN processes the response pattern of individual respondent and generates an Jan 15, 2008 · And do a comparative research of all dynamic parameters GA–SA–BP network model and the Momentum with adaptive learning rate BP model, GA–SA training network model, GA–BP training network model and SA–BP training network model. Python AI: Starting to Build Your First Neural Network. These practical tips are derived from my personal experience with ASHA and May 31, 2021 · To tune the hyperparameters of a neural network, we first need to define the model architecture. They perform some calculations. Apr 1, 2019 · Different from multi-layer neural networks, single-hidden layer neural networks are with a small number of parameters, which simplifies the process of parameter learning. FluCoMa contains two neural network objects, the MLPClassifier and MLPRegressor. For simple feed-forward neural network this would also be the case, but consider that you can increase complexity of a neural network without increasing the number of parameters: you can Oct 4, 2023 · ASHA tends to find better model configuration faster than algorithms (source: the original ASHA paper) Practical tips. Jun 28, 2020 · Neurons in deep learning models are nodes through which data and computations flow. Dec 20, 2020 · This paper investigates the possibility of using Artificial Neural Networks (ANN) to reliably identify tire model parameters. Neural networks are used for a wide range of tasks, including pattern recognition, classification, regression, and decision-making. As a result, reducing the amount of parameters and preserving its competitive performance are always critical tasks in the field of DNN. have associated weights and biases that are optimized during training. In this post, you will […] This is because the parameters of trained small neural networks are not highly concentrated around 0. weight) A neural network is really a program - with many parameters - that simulates a mathematical function. After building the model Aug 4, 2022 · In TensorFlow, the loss function the neural network uses is specified as a parameter in model. 3 m, respectively. They are not set manually. Model Parameters¶ Many layers inside a neural network are parameterized, i. In this chapter, we go through the fundamentals of artificial neural networks and deep learning methods. Compute the loss (how far is the output from being correct) Propagate gradients back into the network’s parameters. of input features. # terminal/zsh/cmd command. The MLP neural network inputs include the voltages, device geometries, temperature, and model parameters. Oct 23, 2019 · A benefit of using maximum likelihood as a framework for estimating the model parameters (weights) for neural networks and in machine learning in general is that as the number of examples in the training dataset is increased, the estimate of the model parameters improves. Neural The parameters are calibrated not only by minimizing the squared residuals over specified collocation points, but the two transport equations are also embedded to constrain possible neural network solutions. We refer to this approach as the neural net estimator (NNE). In this post, you will discover how to use the grid search capability from the scikit-learn Python machine learning library to tune the hyperparameters of Keras’s deep Jul 9, 2019 · In this article, we will be optimizing a neural network and performing hyperparameter tuning in order to obtain a high-performing model on the Beale function — one of many test functions commonly used for studying the effectiveness of various optimization techniques. Subclassing nn. Hyperparameter tuning is the process of selecting the optimal values for a machine learning model’s hyperparameters. Who governs the change? Well, the training algorithm you choose, particularly the optimization strategy makes them change their values. Linear layers by using the method below: def reset_weights(self): torch. Efficient and accurate acquisition of sensitive parameters is the key to real-time model calibration. Differential Evolution Algorithm based Hyper-Parameters Selection of Transformer Neural Network Model for Load Forecasting Abstract: Accurate load forecasting plays a vital role in numerous sectors, but accurately capturing the complex dynamics of dynamic power systems remains a challenge for traditional statistical models. Once a Sequential model has been built, it behaves like a Functional API model. Consider you are building a neural network as shown below: This neural network is overfitting on the training data. This is how we can access and confirm the total number of learnable parameters in a CNN in Keras, as well as see what type of impact these Jun 5, 2023 · Further, branched learning requires fewer parameters and results in faster model training due to better convergence during the training phase than existing neural networks, thereby efficiently Aug 6, 2019 · A node, also called a neuron or Perceptron, is a computational unit that has one or more weighted input connections, a transfer function that combines the inputs in some way, and an output connection. In this case, the Pacejka’s “Magic Formula” has been chosen for the identification due to its complex mathematical form which, in principle, could result in a more difficult learning than other formulations. Artificial neural networks (ANNs) are computational models inspired by the human brain. Learn essential techniques for tuning hyperparameters to enhance the performance of your neural networks. In total, ResNet-50 has 177 layers. To illustrate this, consider the three-layer neural network below. Update the weights of the network, typically using a simple update rule: weight Aug 4, 2022 · The reason is that neural networks are notoriously difficult to configure, and a lot of parameters need to be set. on shallow neural nets as the machine learning model. layers import Bidirectional from keras. Apr 12, 2024 · This paper presents a novel approach known as the cross estimation network (CEN) for fitting the datasets obtained from psychological or educational tests and estimating the parameters of item response theory (IRT) models. So, the algorithm itself (and the input data) tunes these parameters. However, the convolutional neural network needs to be re-trained when the parameters are adjusted. By connecting these nodes together and carefully setting their parameters An optimizer is one of the two arguments required for compiling a Keras model: You can either instantiate an optimizer before passing it to model. Therefore, using the optimal parameters plays a crucial role in saving computational time and increasing the model Oct 27, 2022 · In this paper, we replace the standard numerical approach of estimating parameters in a mathematical model using numerical solvers for differential equations with a physics-informed neural network (PINN). These input signals can come from either the raw data set or from neurons positioned at a previous layer of the neural net. Module automatically tracks all fields defined inside your model object, and makes all parameters accessible using your model’s parameters() or named_parameters() methods. By applying Bayes' theorem, and enforcing independence between the model parameters and the input, the Bayesian posterior can be written as: p( jD ) = p(D y jD A novel approach known as the cross estimation network (CEN) for fitting the datasets obtained from psychological or educational tests and estimating the parameters of item response theory (IRT) models showed that CEN effectively fit the training data and produced accurate estimates of both person and item parameters. The adversarial samples have the capability of fooling highly proficient Oct 31, 2022 · With the introduction of the backdoor in deep neural networks (DNNs), much research focuses on backdoor attacks and defenses against DNNs. May 15, 2024 · B) For the ANN, we trained the neural network to estimate parameters of the Bayesian inference model, and tested it on the data simulated from the Bayesian inference model with stickiness. Therefore, using the optimal parameters plays a crucial role in saving computational time and increasing the model I have a simple pytorch neural net that I copied from openai, and I modified it to some extent (mostly the input). The first step in building a neural network is generating an output from input data. 4. On the basis of the general regression neural network (GRNN) technique, a parameter identification approach Mar 23, 2018 · 12. Network Weight Initialization The procedure involves deriving the state-space dynamic model, embedding the system's dynamics into a recurrent neural network (RNN) with customized Runge-Kutta cells, obtaining labeled training data, predicting system responses, and estimating dynamic parameters. Let net be an instance of a neural network nn. The network depth is defined as the largest number of sequential convolutional or fully connected layers on a path from the input layer to the output layer. fc1. def count_parameters(model): table = PrettyTable(["Modules", "Parameters"]) total_params = 0. A good rule of thumb to overcome this confusion is as follows: If you have to specify a model parameter manually then it is probably a model hyperparameter. 44 m 2. The main reason to consider CNN is the weight sharing feature, which reduces the number of trainable network parameters and in turn helps the network to enhance generalization and to avoid overfitting. This shrinks the learnable parameters drastically in our output layer from the original 2402 to 602, which contributes to a reduced number of total learnable parameters in the network from 2515 to 715 . When I run my code, the output of the network remains the same on every episode, as if no training occurs. 1 (a). Process input through the network. In the rest of this paper, we will denote the model parameters by , the training set by D , the training inputs by D x, and the training labels by D y. In fact, any parameters within our model which are learned during training via SGD are considered learnable parameters. This article is the third in a series of articles aimed at demystifying neural networks and outlining how to design and implement them. Example: from prettytable import PrettyTable. ( U x t + W s t − 1) o t = s o f t m a x ( V s t) Assume that the vocabulary size is m m and that of the hidden layer is n n. 8 m wide and 16 m long, and the ridge and gutter heights are 4. Jan 27, 2022 · We use the MLP neural network to build a device model for parameter extraction. The network is 50 layers deep. On top of that, individual models can be very slow to train. I'm using a basic RNN as in the figure below (say for translation). Schmidt neural network (SNN) ( Schmidt et al. Inferring model posterior with these networks, however, is a difficult task, but different approximations have been introduced to facilitate its computation. Aug 20, 2019 · In this paper, a novel optimization approach, namely neural network algorithm (NNA) is applied for an estimation of the unknown PEMFC model parameters. xavier_uniform_(self. Jun 27, 2019 · Example of non-convex loss surface with two parameters. Unlike these parameters, hyperparameters must be set before the training process starts. In this case, the Pacejka's "Magic Formula" has been chosen for the Feb 7, 2021 · Weight initialization is an important consideration in the design of a neural network model. They are estimated by optimization algorithms (Gradient Descent, Adam, Adagrad) They are estimated by hyperparameter tuning. We looked at the correlation between the ground truth parameters (from a separate test set), and the predictions of the network trained on the model without Deep neural networks (DNN) have achieved great success in machine learning due to their powerful ability to learn and present knowledge. After the qualitative discussion above, we proceed to discuss how the network behaves over the entire parameter space. This has the effect of stabilizing the learning process and dramatically reducing the number of training epochs required to train deep networks. Each node's output is determined by this operation, as well as a set of parameters that are specific to that node. Module . This means that every layer has an input and output attribute. The CEN is comprised of two subnetworks: the person network (PN) and the item network (IN). They are weight matrices that contribute to model’s predictive power, changed during back-propagation process. It is, of course, parametrized by 2n+2 weights: n weights for each input neuron and 2 weights for the output neuron. Neural networks behave differently than linear regression models; their loss function is non-convex and can have multiple minima even when training sets are large. “MLP” stand for multi-layer perceptron, which is a type of neural network. named_parameters() that returns an iterator over both the parameter name and the parameter itself. Neural networks have universal approximation properties, meaning they can approximate any function in any In case of simple models, like linear, or logistic regression this is simple, as the number of regression parameters determines the complexity of the model. For an electromagnetic (EM) wave and plasma interaction system, it is common to retrieve plasma parameters based on the reflected or scattered EM field, whereas multiple parameter inversion becomes particularly challenging for anisotropic inhomogeneous plasma medium Jul 25, 2017 · Model hyperparameters are often referred to as model parameters which can make things confusing. We can get the Aug 6, 2019 · Dropout regularization is a generic approach. The model parameters can be calibrated according to: This article provides guidance on using the parameters of the neural networks found in the FluCoMa toolkit. Nov 26, 2018 · The test algorithm is used to determine the geotechnical parameter prediction model as a four-layer BP neural network model of 4-10-1. Note: There is also a bias unit in a feed-forward neural network in all the layers except the output layer. I can do so for nn. You are likely to get better performance when dropout is used on a larger network, giving the model more of an opportunity to learn independent representations. Nodes are then organized into layers to comprise a network. Suppose we add a dropout of 0. model. May 10, 2023 · In this research, the hyperelastic strain energy density function based on the exponential–logarithmic invariant is extended to the visco-hyperelastic constitutive model to describe the mechanical characteristics of the rate dependence and large deformations of rubber-like materials. The total ground area covered by the greenhouse (A g) is equal to 204. hk mu iu rn lj lh vm si nn io
